The OP is the very definition of a solution looking for a problem.
Because the earth is spinning just barely faster.
Stupid Moon trying to ruin our life.
I think this is an important issue, and thank the OP. However, as Chronos points out, there is a well established convention. Similarly, we truncate time (or date) when we state our age, and consider it incorrect to round up when we are less than 6 months from our next birthday.
Timekeeping is cool. I used to do complicated industrial experiments with multiple data acquisition systems and needed subsecond accuracy when matching subsystems. It galls me that I can’t tell my iPhone to always include seconds when displaying timestamps.
I doubt it
The tidal drag of the moon slowing the earth’s rotation, while the dominant force over the very long term, is not actually the most significant force modifying the earth’s speed of rotation over shorter time frames. That stronger force is redistribution of earth’s mass to or from the poles and equator combined with conservation of angular momentum. For example, during a glaciation period, sea levels drop and that water is frozen at high latitudes, which are closer to the axis of rotation, resulting in faster rotation and shorter days. Then the glaciers melt, and the opposite happens. And then after the glaciers have melted, you have the isostatic rebound of the earth’s crust which changes the mass distribution again. We are still in an isostatic rebound phase, and we’re also melting the polar ice caps, both of which have more impact on the length of days year-to-year than tidal friction.
Stupid Earth trying to ruin our life.
There is even a measurable effect caused by human activity. Dams that sequester large bodies of water can redistribute enough mass to change the speed of Earth’s rotation.
ETA @Saint_Cad
Yeah. But we’ll show it! Here Earth, take another 5C of warming! See how you like that!,!?
BWAAA HAA HAAA!
That’s actually brilliant. As it gets warmer Earth gets less dense by conservation of momentum it speeds up thus canceling out the slowing.
Well well well – we can’t trust time.gov. I just tried it again, and the display now changes a noticeable fraction of a second early – dunno if it’s a full half-second. What’s the easy way to compare them, sound against screen?
(I.e., screen display against 303-499-7111, which presumably has the correct UTC.)
you’re scaring me now.
My nap is ruined.
Thanks universe. 
You’re on a dead end errand.
The random delays in the phone system cannot be controlled for. The random delays on the internet can be controlled for to a smaller (but still non-zero) error delta than a human can perceive.
Time.gov is right enough for any real purpose you might have. All other time sources are more wrong than it is. Nothing more can usefully be said unless you want to start buying serious expensive gear or paying for way upstream access.
Metrology is a very deep subject; we have a retired metrologist here somewhere; shame I forget his handle. And of all the fundamental standards, time is one of the harder ones.
“Time is an illusion. Lunchtime doubly so.” — Douglas Adams
Stranger
So you figure 303-499-7111 isn’t reliable – but probably WWV on the shortwave is? (10 MHz most likely; 5 MHz if 10 MHz doesn’t come in well.)
I don’t have a shortwave radio any more – I’d be curious to see how unreliable the phone is.
Compare the phone to time.gov. Done. You do you, but IMO all else is mental masturbation to no actual useful knowledge.
The NTP protocol uses a clever algorithm to factor out network delays, so the client gets a time that is accurate to much less than the network delay. However, it depends on the delay being consistent during the NTP request (client-to-server) and the response (server-to-client). In an environment with asymmetric delays or delays that vary over time, even NTP won’t deliver accurate results.
Meaning, being off by a half-second won’t bother anyone?
If you’re at latitude 38 North, the sun’s azimuth at noon changes by about 10 arc seconds in a half second of time (less in December, more in March/September). So if you’re determining true north, and you want to do it in the daytime, guess you’re stuck with shortwave WWV.
Doesn’t bother me in the least.
The only thing that’s perfect is imperfection.